Negative impedance circuits



Oct. 21, 1930. H. w; DUDLEY NEGATIVE IMIfEDANCE CIRCUITS Filed Au 1,1927 15 have appeared not to be meme a, 21; 1930 UNITED STATES T T.OFFICE norms w. DUDLEY, or BROOKLYN, imw YORK, Assumes TO BELL mmnonmom'ronms, mconromm, or NEWVYORK, N. "1., A ooaronsnon or msw- YORKREGA'rivE mrmmncn omcun's This invention relates to a method and meansfor obtaining negative impedance and particularly to vacuum tubecircuits for that purpose. I

An object of the invention is to produce two different types of negativeimpedance in the same electrical circuit. 1

A further object is to combine these different types of negativeimpedance to-pro- 1o duce advantageous results in a telephone repeater.

From time to time in the design of theoretical networks for specialtransmission purposes, solutions have been obtained which hysicallyrealizable because they contained terms equivalent to negativeinductances and negative capacities, as Well as negative resistances.The copending application of R. C. Mathes," Serial No. 209,752, filedAugust 1', 1927, discloses a circuit for obtaining a negative impedancewhich is the negative at all frequencies of any positive impedance whichcan be constructed physically. This circuit in a pre- 2:, ferredembodiment is an amplifier comprising two three-electrode vacuum tubestages, resistance-coupled, the input circuit of the first stage beingshort-circuited, and a 'feed back impedance connected between the out-::o put circuit of the last tube and the input circuit of the first tubein the amplifier. In this circuit, when an electromotive force isimpressed across terminals connected respectively to the input circuitof the first 3; tube between the grid thereof and the feed backimpedance, andto the plate of the last tube, any desired negativeresistance, negative inductance, negative ca acity, or any complexcombination thereo may be ob- 40 tained across the terminalsby'utllizing as the feed back impedance a similar network of positiveelements having a ratio to the desired elements determined solely by thevarious constants of the amplifier circuit.

The copending application referred to also discloses a modification ofthe above described circuit necessitating only one vacuum tube in whichthe feed back impedance isapplied between the plate circuit and gridcircuit of the same tube, a transformer of neglible distortion in phaseand amplitude bein inserted between the grid circuit and the eed backimpedance, the negative impedance in this case being obtained betweenterminals connected respectively to the plate of the tube and oneterminal of the feed back impedance.

In both of the circuits of the copending application-referred to, thenegativeimpedance obtained, whenutilized to balance the effect ofpositive impedance in an electrical circuit connected across thenegative impedance terminals, has been found to be stable only when theconstants of the circuits are selected so that the net impedance of thecombined circuits is positive; that is the positive impedance of thecircuit it faces in order to prevent singing.

In accordance with the present invention -it has'been found that eitherof the above described circuits besides being utilized to obtain thenegative impedance having the characteristics set forth, may be utilizedalso at the same time to produce between two other oints in the samecircuit, another negative 1m edance having different characterhe newtypeof negative impedance circuit connected across these terminals, it

is stable only when the net impedance of the combined circuits isnegative,that is, when the constants of the circuits are so selectednegative impedances must be less than the that the negative impedanceacross the feed back "impedance terminals is greater than the positiveimpedance of the circuit it faces to prevent sing1ng.-

A practical application of the circuits of the invention is a repeateradapted for repeating a 'message in two opposite directions with the useof one repeater element. The repeater in this case is formed bybalancing the two telephone lines against each other, one line beingconnected to the particular terminals of the amplifier circuit acrosswhich is produced one type of negative impedance and the other to theterminals thereof across which is produced the other type of negativeimpedance. The repeater thus formed acts for transmission in onedirection effectively as a series booster, while for transmission in theopposite direction, it is equivalent'to a shunt booster.

The various objects and features of the invention will be understoodfrom the following detailed description thereof, when read in connectionwith the accompanying drawing, in which the single figure shows cathodes3 and 6 respectively 0 tubes 1 and 2 are connected together and may beheated by a common battery 9. The output circuit of tube 1 and the inputcircuit of tube 2 are coupled through coupling resistance 10 common tothe circuits. The battery 11 supplies space current'to the plate 4 oftube 1 through coupling resistance 10, and space current to the plate 7of tube 2 through resistance R The battery supply resistances 10 and Rpreferably are made non-inductive and noncapacitive. The grid potentialsof tubes 1 and 2 are adjusted to any suitable values by grid batteries12 and 13 in the respective input circuits of the tubes.

The grid 5 of tube 1 isconnected through branched paths respectively toa terminal' l l and through conductor 15 to a terminal 16.

The cathode 3 of tube 1 is connected directly to a terminal 17. Aterminal 18 is connected through a battery 19 to a point in the outputcircuit of tube 2 between the anode 7 thereof and the resistance R Thebattery 19 is poled so as to oppose the effect of space current battery11 and its voltage is made equal to the voltage of space current battery11 less the potential drop in resistance R L represents a telephone linehaving a characteristic impedance represented by the box Z, theterminals 21 and 22 of which line are adapted to be connected across theterminals 14 and 17 of the amplifier circuit, and L represents a secondtelephone line having a characteristic impedance represented by abovedescribed, it will be assumed that the line L, is coupled in suitablemanner by its terminals 21 and 22 to the terminals 14 and 17 of theamplifier, and that line L is connected by its terminals 23 and 24 tothe terminals 16 and 18 of the amplifier circuit. 7

To simplify the explanation of the operation of the circuit, it will beassumed that the impedance 2 of line L is zero and that an electromotiveforce 0 is applied by the line L to terminals 16 and-18 of the amplifiercircuit in such a manner as to drive a current I in the directionindicated by the solid arrow to the left of the figure through conductor15, impedance Z of telephone'line L and through R, and R (the internalresistance of the space path of tube 2) in parallel. It is also assumedthat the impedance Z of line L connected across the terminals 21 and 22of the amplifier has a finite value, no electromotive force bei gapplied acrom these terminals. The resu tant drop of potential inimpedance Z due to the current flowing therein will be impressed on thein? put circuit of the amplifier across grid 5 and cathode 3 of tube 1.This voltage will be amplified in the amplifier circuit, and the voltageset up thereby in tube 2 of the amplifier will cause a, current to flowin the outputcircuit of that tube in the direction away from the anode7. Because of the high impedance of resistance R thereto, most of thiscurrent, which will be desig nated at I,,,, is transmitted throughbattery 19, the impedance 2 of line L conductor 15, and impedance Z oftelephone line L in the same direction, as indicated by the dottedarrow, as the original current I due to the voltage 6 impressed acrossthe terminals 16 and 18.

The effect, therefore, is to produce a cur rent flowing through thepositive impedance in the circuit (which is where R, is the A. C. platecircuit resistance of tube 2), which current is in phase with that dueto the voltage e alone applied across the terminals 16 and 18. When thetotal current is greater than the latter current the offeet is one ofinserting across these terminals an impedance 2', which, as will beexplained later, may be made any desired negative impedance. The valueof the impedance 2', as is shown in the copending application of R. C.Mathes referred to, depends solely on the values of the constants. ofthe amplifier circuit, and may be expressed in terms of the resistance Rthe impedance Z, the net volt- IOU age amplification M from the grid oftube 1 v of negative, impedance for a may be obtained at terminals 16and 18 by suitably selecting the relative values of the elements givenin the equations. p I

It has been determined, however, that to 1 prevent singing effects inthe circuit described, it is necessary that the circuit elements be soselected that the negative of the impedance 2' is in general less thanthe positive impedance 2: in the circuit which it faces, in other words,so that the net impedance of the combined circuits is positive.

The portion of the circuit of the drawing which has been described aboveis identical with that disclosed and claimed in the copending.application of R. C. Mathes referred to, supra.

Now in accordance with this invention means are provided forobtaining'between planation of the operation ofthis part of this of thedrawing.

portion. of the circuit in obtaining this different type of negativeimpedance, it. will be assumed that an electromotive force e is ap pliedby the telephone line L across the terminals 14 and 17 of the amplifiercircuit, and

that the impedance'Z of the line L equalszero. It is assumed also thatthe impedance 2 of line L connected across the terminals 16 and 18 ofthe amplifier has a finite value, no electromotive force in this casebeing applied across these terminals.

It will be assumed that the electromotive force 2' drives a current I,through the cir cuit including R and R in parallel, and impedance z oftelephone line L in the direc tion indicated by the solid arrow to theright The resultant drop in potential in impedance 2 will cause anincrease in the negative potential of grid 5 of tube 1,

resulting in a voltage being set up in the last tube of the amplifier,tube 2, which will cause a current to flow in the output circuit of thattube in the direction away from its anode. Because of the high impedanceof resistance R thereto, most of this current, which may be designatedas 1 will flow through the battery 19 and the impedance z of telephoneline L as indicated by the dotted arrow, in the direction opposite tothat of the original current I, due'to the voltage 6 impressed on theamplifier by telephone line L Now if the constants of the amplifiercircuit are so selected that the current I driven through the impedance2 by the voltage set up in tube 2 of the amplifier is made larger thanthe current I," due to the voltage e impressed across the terminals 14and 17, the resultant current in impedance 2 of telephone line L willflow in the-direction opposite to that due to the impressedelectromotive force 6. This means that in effect a negative impedance Zis'produced across the terminals 14 and 17, facing the impressed E. M.F. This negative impedance Z, it has been found, has suchcharacteristics that it must in general be greater in magnitude than thepositive impedance Z it faces to prevent singing in the circuit. 'lVhenthe constants of the circuit. are so selected that the current I is lessthan the current I, the resultant current flowing through the impedance2 is decreased so that the effect is one of multiplying an impedance bya value greater than unity.

The circuit illustrated and described above forms'a novel form of 21type repeater in which the impedances Z and ,2, respectively, of twotelephone lines are balanced against each other. For proper operation,the constants ofthe amplifier circuit and that of the telephone line areselected so that its net impedance is negative for Z +Z and ositive for2+z'. Accordingly, this pro uces the effect that for transmission fromline L .line L the signaling currents have the same direction with theamplifier in the circuit as with it but, whereas for transmission fromline L to lineL the signaling current in-the receivingline L is oppositein direction to that which would be obtained ifathe repeater wereomitted. Therefore, for transmission in one direction the amplifierarrangement operates as a series booster,

while for transmission in the opposite direction, the amplifier isequivalent to a shunt booster.

The theory on which the operation of the above .described circuit isbased will be clear from the following analysis, in which the charactersused in the equations are the same as those referred to in the previousdescription. i

The fundamental equations for the circults shown in the drawing are:

where and From Equation (4) it is seen that R is I always a positiveresistance. K is a positive real number when From Equation (1) it isseen that 2 can be made the negative of any positive lmpedance Z bymaking Z .R K K similarly from Equation (2) Z, Z0 if 2 KZO so that byadding the resistance in series with Z, the impedance is made Z asdesired.

From the foregoing, it is seen that any de sired negative impedance maybe obtained as a driving point impedance from either of two points inthe circuit of the drawing. This negative impedance may be used asanother impedance would be so long as the system retains approximatelylinear currentvoltage relations, i. e., the tubes are not overloaded andthe circuit does not sing.

)Ve will now consider the repeater application in which Z and z are thepositive impedances of telephone lines. Here the conditions for allrepeater gains, i. e.,

z= 2; Z Z (8) will be examined. Substituting from Equation (8) inEquations (1) and (2), both equations reduce to Kz=z+R 9) The resistancecan of course be added on K=1 and Z=z+R (10) in this case are easilycalculated since'the same current must flow through both Z and .2. Withan electromotive force 0 in Z, the current is while with anelectromotive force e in impedance 2, the current 1s so that changing Mchanges the gains in the two directions giving an unsymmetricalrepeater.

If M=2 then i=i', so that this is the condition for equal amplificationin the two directions. The Equation 12 shows, however, that a resistancein series with z or Z can be used to control the gain. As this does notchange. M the gain in the two directions is changed by the same amount.

It is to be understood, that in accordance with the invention, anysuitable means other than the means shown may be utilized for separatingthe A. C. and D. C. paths in the output circuit of the tubes forobtaining the two types of negative impedance, for example, condensers,repeating coils or inductances may be used for this purpose.

The telephone repeater formed by balancing two telephone lines againsteach other, as described above, utilizes a resistance coupled amplifierof two stages for obtaining the two impedances of differentcharacteristics facing the telephone lines. It is apparent, however,that the type of circuit disclosed in Fig. 2 of the Mathes applicationreferred to, in which only one vacuum tube is used, the impedance feedback being applied between the plate and grid circuits of the same tubethrough a transformer of negligible distortion in phase and amplitude,may be utilized also for forming the novel form of repeater describedabove. I f such an amplifier is used, one of the telephone lines shouldbe connected across the feed back terminals and the other line connectedbetween the plate of the tube and the primary winding of thetransformer.

The system above illustrated and described should be considered merelyas typical and not as limiting the invention, the scope of which isdefined in the appended claims.

What is claimed is:

1. The method of obtaining the negative of a given reactive impedance ina circuit comprising the given impedance and a source of electromotiveforce comprising deriving a voltage from the circuit, proportioned withrespect to the value of said reactive impedance, amplifying the voltageand applying the amplified voltage to the original circuit in out ofphase relation to the source of volt from the drop of potential in saidimpedance, amplifying the derived voltage and applying the amplifiedvoltage to the circuit in out of phase relation to the voltage of saidsource, the'amplified voltage being of suflicient magnitude to producein the circuit current of greater amplitude than would be produced bythe said source of voltage.

3. The method of securing the negative of a desired reactive impedancebetween a pair of terminals in a circuit comprising constructing apositive impedance similar in characteristics to the impedance thenegative of whichis desired, deriving a voltage from the drop ofpotential in said positive impedance'in circuit with a source ofvoltage, am

plifying the derived voltage and applying the amplified voltage to saidcircuit in series with said pair of terminals and said positiveimpedance in out of phase relation to the voltage of said source ofvoltage, the amplified voltage being of suflicient magnitude to producein the circuit current of greater amplitude than would be produced bythe said source of voltage acting throughsaid positive impedance.

4. The method of effectively increasing the eflective value of a givenreactive impedance, comprising derivinga voltage from a c1rcu1t lncludmgthe given reactlve impedance anda source of potential, proportioned withrespect to the value of said given impedance, amplifying the derived,voltage, and applying the amplified voltage to said circuit inout-of-phase relation to the voltage of said source, the amplificationbeing of a degree to produce in'the circuit a smaller current flow thanwould be produced 'by said source of voltage acting through the givenimpedance.- 7 W 5. A combination for obtaining a negative impedance ofcertain definite characteristics between the terminals of an electricalcircuit including a source of electromotive force, said combinationcomprising an amplifier circuit consisting of a space discharge devicehaving an input circuit and an output circuit, an impedance network insaid inputcircuit, the terminals of said network being connected acrossthe terminals of said electrical circuit and across said source ofelectromotive force independently of said amplifier circuit, and meansfor feeding. back the amplified '1tages from said output circuit .ofsaid' de vice to the input circuit thereof across said 66 impedancenetworkin phase with the e'lec-l .work, said terminals of saidelectrical circuit tromotive force impressed thereon, thecharacteristics of said negative impedance thus] obtained between saidterminals of said electrical circuit being such that said negativeimpedance is stable only when the net impedance of'the combined circuitsis negative.

6. Means for obtaining a negative impedance between two terminals of anelectrical circuit comprising, a three-electrode space discharge devicehaving an input circuit and an output circuit, means comprisin an im--pedance network having terminals %or feeding back the amplified voltagesproduced in the output circuit of said space discharge de- Woe to theinput circuitthereof, means for producing a 180 phase shift of the fedback Voltages, and a conductive'connection independent of said devicefrom each of said electrical circuit terminals to a different terminalvof said impedance network. '7. Means for obtaining a negative impedancebetween two terminals of an electrical circuit comprising an impedancenetwork connected between said terminals by connections of negligibleimpedance, an amplifier consistingof an even number of vacuum tubestages and having an input circuit and an output circuit, said impedancenetwork being connected directly in said output circuit comprising anamplifier consisting of an even number ofspacedischarge devicesresistance coupled, the outputof the last space discharge device in saidamplifier being coupled to the input circuit of the first device in saidamplifier through an impedance netbeing connected across said. impedancenetwork, independently of said amplifier, the negative impedanceobtained between said terminals having such characteristics that it nois stable only whenits value, which is determined solely by theconstants of said ampli- -fier,exceeds that of the positive impedance insaid electrical circuit which it faces.

9. Means for obtaining a negative impedance of certain definitecharacteristics between two terminals of an electrical circuitcomprising an amplifier consisting of an even number of space dischargedevices, re-

sistance coupled, each ofsaid space discharge devices having an inputand an output-circuit and having a cathode, an anode and a. controlelectrode, an impedance network coupling the output circuit of the lastspace discharge device in said amplifier-to the inm put circuit of thefirst space discharge device in said 'amplifier, a connection from oneof said terminals to said input circuit of said first discharge devicebetween the cathode 'thereof'and one end of said impedance net-- nowork, and a second connection-from the other of said terminals to saidinput circuit of said first device between the cathode thereof andnegative impedance having different charact-eristics, one of said linesbeing connected between the first mentioned two terminals and the otherof said lines being connected between the other of said terminals, saidcertain characteristics of the first mentioned negative impedance beingsuch that it is stable only when it is greater than the positiveimpedance of the line which it faces, and said different characteristicsof the last mentioned negative impedance being such that it is stableonly when it is less than the positive impedance of the line it faces. g

11. A telephone repeater for repeating signaling currents in eitherdirection between two lines comprising a single amplifier circuit,providing between two terminals thereof connected across one of saidlines a negative impedance which for stability necessitates that itshould be greater than the positive impedance of the line it faces, andproviding between two other terminals thereof a negative impedance whichfor stability necessitates that it should be less than the positiveimpedance of the line it faces.

12. A repeater for repeating signaling currents in either directionbetween two telephone lines comprising an amplifier and having suchcharacteristics that for transmission between the lines in one directionthe current has the same direction in the receiving line with theamplifier in as with it out and for transmission in the oppositedirection, the current in the receiving line is opposite in direction tothat which would be obtained if the amplifier were omitted and the twolines were directly connected to each other.

13. A repeater circuit comprising a single amplifier for repeatingsignaling currents in either direction between two lines, said amplifierbeing arranged to give any desired ratio between the amplifications ofthe signaling currents in the two direct-ions of transmission.

14. A repeater circuit comprising a single amplifier for repeatingsignaling currents in I either direction between two lines, andincludcuit proportioned with respect to the value of said impedance,amplifying the derived voltage, and applying the amplified voltage tosaid circuit in out-of-phase relation to the voltage of said source, theamplification of said voltage bein of a degree to produce in saidcircuit the e ect of said impedance multiplied by a real negativefactor.

In witness whereof, I hereunto subscribe my name this 28 da of July, A.D'. 1927.

Hal ER W. DUDLEY.

comprising deriving a voltage from said cir-

